8. Bibliography
- 1
Patrick K Notz, Roger P Pawlowski, and James C Sutherland. Graph-based software design for managing complexity and enabling concurrency in multiphysics pde software. ACM Transactions on Mathematical Software (TOMS), 39(1):1–21, 2012.
- 2
Michael L. Hobbs, Judith A. Brown, Michael J. Kaneshige, and Cuauhtemoc Aviles-Ramos. Cookoff of powdered and pressed explosives using a micromechanics pressurization model. Propellants, Explosives, Pyrotechnics, 47(2):e202100156, 2022. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/prep.202100156, arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/prep.202100156, doi:https://doi.org/10.1002/prep.202100156.
- 3
W. M. Deen. Analysis of Transport Phenomena. Topics in Chemical Engineering. Oxford University Press, New York, 1998.
- 4
Lawrence E. Malvern. Introduction to the Mechanics of a Continuous Medium. Series in Engineering of the Physical Sciences. Prentice-Hall, Upper Saddle River, NJ, USA, 1969.
- 5
George E. Mase. Theory and Problems of Continuum Mechanics. Schaum's Outline Series. McGraw-Hill, New York, NY, USA, 1970.
- 6
Javier Bonet and Richard D. Wood. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press, 1997.
- 7
Ted Belytschko, Wing Kam Liu, and Brian Moran. Nonlinear Finite Elements for Continua and Structures. John Wiley and Sons, 2004.
- 8
M. J. Martinez. Mathematical and numerical formulation of nonisothermal multicomponent three-phase flow in porous media. Technical Report SAND95-1247, Sandia National Laboratories, Albuquerque, NM, USA, 1995. http://www.prod.sandia.gov/cgi-bin/techlib/access-control.pl/1995/951247.pdf.
- 9
M. J. Martinez, P. L. Hopkins, and J. N. Shadid. LDRD final report: physical simulation of nonisothermal multiphase multicomponent flow in porous media. Technical Report SAND97-1766, Sandia National Laboratories, Albuquerque, NM, USA, 1997. http://www.prod.sandia.gov/cgi-bin/techlib/access-control.pl/1997/971766.pdf.
- 10
M. J. Martinez, P. L. Hopkins, and P. N. Reeves. PorSalsa user's manual. Technical Report SAND2001-1555, Sandia National Laboratories, Albuquerque, NM, USA, 2001. http://www.prod.sandia.gov/cgi-bin/techlib/access-control.pl/2001/011555.pdf.
- 11
Chris Lautenberger and Carlos Fernandez-Pello. Generalized pyrolysis model for combustible solids. Fire Safety Journal, 44(6):819–839, 2009.
- 12
D. K. Gartling, C. E. Hickox, and R. C. Givler. Simulations of coupled viscous and porous flow problems. Comp. Fluid Dyn., 1-2:23–48, 1997.
- 13
S. A. Roberts, D. R. Noble, E. M. Benner, and P. R. Schunk. Multiphase hydrodynamic lubrication flow using a three-dimensional shell finite element model. Comput. Fluids, 2013. , in press.
- 14
Ely M Gelbard. Application of spherical harmonics method to reactor problems. Bettis Atomic Power Laboratory, West Mifflin, PA, Technical Report No. WAPD-BT-20, 1960.
- 15
A. D. Kraus and A. Bar-Cohen. Thermal Analysis and Control of Electronic Equipment. Hemisphere, Washington DC, 1983.
- 16
J. H. Lienhard IV and J. H. Lienhard V. A Heat Transfer Textbook. Phlogiston Press, Cambridge, Massachusetts, 3rd edition, 2004. URL: http://web.mit.edu/lienhard/www/ahtt.html.
- 17
C. V. Madhusudana. Thermal Contact Conductance. Springer-Verlag, New York, 1996.
- 18
R. Siegel and J. R. Howell. Thermal Radiation Heat Transfer. Taylor and Francis, Washington, D.C., 1992.
- 19
M. W. Glass. Chaparral: a library for solving enclosure radiation heat transfer problems. Technical Report SAND01-xxxx, Sandia National Laboratories, Albuquerque, New Mexico, 2001.
- 20
B. R. Carnes and K. D. Copps. Thermal contact algorithms in sierra mechanics. Technical Report SAND2008-2607, Sandia National Laboratories, Albuquerque, New Mexico, April 2008.
- 21
D.N. Arnold, B. Cockburn, and L. D. Marini. Unified analysis of discontinuous galerkin methods for elliptic problems. SIAM J. Numer. Anal., 39:1749–79, 2002.
- 22
E. B. Becker, G. F. Carey, and J. T. Oden. Finite Elements: An Introduction. Prentice-Hall Inc., New Jersey, 1981.
- 23
T. R. Young. Chemeq—a subroutine for solving stiff ordinary differential equations. Technical Report NRL Memorandum Report 4091, Naval Research Laboratory, Washington D.C., 1980.
- 24
B. A. Finlayson. The Method of Weighted Residuals and Variational Principles. Academic Press, New York, 1972.
- 25
P. Gresho, R. Lee, R. Sani, and T. Stullich. On the time-dependent FEM solution of the incompressible navier-stokes equations in two and three dimensions. Recent Advances in Numerical Methods in Fluids, 1980.
- 26
D. K. Gartling, R. E. Hogan, and M. W. Glass. Coyote—a finite element computer program for nonlinear heat conduction problems, part I—theoretical background, version 4.05. Technical Report SAND94-1173, Sandia National Laboratories, Albuquerque, New Mexico, 2000.
- 27
D. K. Gartling, R. E. Hogan, and M. W. Glass. Coyote—a finite element computer program for nonlinear heat conduction problems, part II—user's manual, version 4.05. Technical Report SAND94-1179, Sandia National Laboratories, Albuquerque, New Mexico, 2000.
- 28
J. E. Marsden and A. J. Tromba. Vector Calculus. W. H. Freeman and Company, New York, 1981.
- 29
S. Domino. Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach. J. Comp. Phys, 359:331–351, 2018.
- 30
S. Domino, P. Sakievich, and M. Barone. A assessment of atypical mesh topologies for low-Mach large-eddy simulation. Comp. Fluids, 179:655–669, 2019.
- 31
Robert Moser, editor. Numerical Methods in Turbulence Simulation. Computation and Analysis of Turbulent Flows. Academic Press, San Diego, CA, December 2022.
- 32
Guglielmo Scovazzi and T Hughes. Lecture notes on continuum mechanics on arbitrary moving domains. Lecture Notes, November, 2007.
- 33
Eric C Cyr, John N Shadid, and Raymond S Tuminaro. Teko: a block preconditioning capability with concrete example applications in navier–stokes and mhd. SIAM Journal on Scientific Computing, 38(5):S307–S331, 2016.
- 34
Rafael Martí and Gerhard Reinelt. The linear ordering problem: exact and heuristic methods in combinatorial optimization. Volume 175. Springer Science & Business Media, 2011.
- 35
Irene Charon and Olivier Hudry. A branch-and-bound algorithm to solve the linear ordering problem for weighted tournaments. Discrete Applied Mathematics, 154(15):2097–2116, 2006.
- 36
G. S. Beavers and D. D. Joseph. Boundary conditions at a naturally permeable wall. J. Fluid Mech., 30:197–207, 1967.
- 37
P. G. Saffman. On the boundary condition at the surface of a porous medium. Studies in Applied Mathematics, 50(2):93–101, 1971.
- 38
R. H. Davis and H. A. Stone. Flow through beds of porous particles. Chemical Engineering Science, 48(23):3993–4005, 1993.
- 39
James A Sethian. A fast marching level set method for monotonically advancing fronts. Proceedings of the National Academy of Sciences, 93(4):1591–1595, 1996.
- 40
David R Noble, Elijah P Newren, and Jeremy B Lechman. A conformal decomposition finite element method for modeling stationary fluid interface problems. International Journal for Numerical Methods in Fluids, 63(6):725–742, 2010.
- 41
Bruno Lafaurie, Carlo Nardone, Ruben Scardovelli, Stéphane Zaleski, and Gianluigi Zanetti. Modelling merging and fragmentation in multiphase flows with surfer. Journal of computational physics, 113(1):134–147, 1994.
- 42
Richard A Cairncross, P Randall Schunk, Thomas A Baer, Rekha R Rao, and Phillip A Sackinger. A finite element method for free surface flows of incompressible fluids in three dimensions. part i. boundary fitted mesh motion. International journal for numerical methods in fluids, 33(3):375–403, 2000.
- 43
S Hysing. A new implicit surface tension implementation for interfacial flows. International Journal for Numerical Methods in Fluids, 51(6):659–672, 2006.
- 44
D. Dobranich. Safsim input manual -a compute program for the engineering simulation of flow systems. Technical Report SAND92-0694, Sandia National Laboratories, Albuquerque, NM, USA, September 1992.
- 45
Eric C Cyr, John N Shadid, and Raymond S Tuminaro. Stabilization and scalable block preconditioning for the navier–stokes equations. Journal of Computational Physics, 231(2):345–363, 2012.
- 46
Youcef Saad. A flexible inner-outer preconditioned gmres algorithm. SIAM Journal on Scientific Computing, 14(2):461–469, 1993.
- 47
Robert Kosik, Peter Fleischmann, Bernhard Haindl, Paola Pietra, and Siegfried Selberherr. On the interplay between meshing and discretization in three-dimensional diffusion simulation. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 19(11):1233–1240, 2000.
- 48
Changna Lu, Weizhang Huang, and Jianxian Qiu. Maximum principle in linear finite element approximations of anisotropic diffusion–convection–reaction problems. Numerische Mathematik, 127(3):515–537, 2014.
- 49
Dmitri Kuzmin. Linearity-preserving flux correction and convergence acceleration for constrained galerkin schemes. Journal of Computational and Applied Mathematics, 236(9):2317–2337, 2012.
- 50
Dmitri Kuzmina and John N Shadidb. A new approach to enforcing discrete maximum principles in continuous galerkin methods for convection-dominated transport equations. Preprint: Ergebnisberichte des Instituts für Angewandte Mathematik, 2015.
- 51
I. M. Levi. Users' Guide to the Transient Heat Conduction Finite Element Code HTCON. Technical Report MM70-5425-17, Bell Telephone Laboratories, Whippany, NJ, USA, 1970.
- 52
A. F. Emery, K. Sugihara, and A. T. Jones. A comparison of some of the thermal characteristics of finite-element and finite-difference calculations of transient problems. Num. Heat Trans., 2:97–113, 1979.
- 53
F. Damjanic and D. R. J. Owen. Practical considerations for thermal transient finite element analysis using isoparametric elements. Nucl. Engrg. Des., 69:109–126, 1982.
- 54
E. Rank, C. Katz, and H. Werner. On the importance of the discrete maximum principle in transient analysis using finite element methods. Int. J. Num. Meth. Engng., 19:1771–1782, 1983.
- 55
H. S. Carslaw and J. C. Jaeger. Conduction of Heat in Solids. Clarendon Press, Oxford, 2\textsuperscript nd edition, 1959.
- 56
I. M. Krieger. Rheology of monodisperse latices. Adv. Colloid Interface Sci., 3:111–136, 1972.
- 57
D. K. Gartling. NACHOS II - a finite element computer program for incompressible flow problems. part I - theoretical background. Technical Report SAND86-1816, Sandia National Labs, Albuquerque, NM, USA, April 1986.
- 58
E. R. G. Eckert. Survey of boundary layer heat transfer at high velocities and high temperatures. Technical Report, WADC, 1960.
- 59
Clark R. Dohrmann and Pavel B. Bochev. A stabilized finite element method for the Stokes problem based on polynomial pressure projections. Int. J. Num. Meth. Fluids, 46:183–201, 2004.
- 60
Pavel B. Bochev, Clark R. Rohrmann, and Max D. Gunzburger. Stabilization of low-order mixed finite elements for the Stokes equations. SIAM J. Numer. Anal., 44(1):82–101, 2006.
- 61
T. Hughes, L. P. Franca, and M. Balestra. A new finite element formulation for computational fluid dynamics: v. circumventing the babuska-brezzi condition: a stable petrov-galerkin formulation of the stokes problem accomodating equal-order interpolations. Comput. Methods Appl. Mech. Engrg., 59:85–99, 1986.
- 62
S. Gordan and B. J. McBride. Computer program for calculation of complex chemical equilibrium compositions and applications I. analysis. Technical Report Ref. Publication 1311, NASA, October 1994.
- 63
B. J. McBride and S. Gordan. Computer program for calculation of complex chemical equilibrium compositions and applications II. users manual and program description. Technical Report Ref. Publication 1311, NASA, June 1996.